Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regions
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Abstract (arXiv)
Stability guarantees are crucial when ensuring that a fully autonomous robot does not take undesirable or potentially harmful actions. We recently proposed the Neural Contractive Dynamical Systems (NCDS), which is a neural network architecture that guarantees contractive stability. With this, learning-from-demonstrations approaches can trivially provide stability guarantees. However, our early work left several unanswered questions, which we here address. Beyond providing an in-depth explanation of NCDS, this paper extends the framework with more careful regularization, a conditional variant of the framework for handling multiple tasks, and an uncertainty-driven approach to latent obstacle avoidance. Experiments verify that the developed system has the flexibility of ordinary neural networks while providing the stability guarantees needed for autonomous robotics.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 26 of its 61 references that are in the map. First posted on arXiv 18 Nov 2024.
Builds on
26 of 61 references.
References · 26
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2020How Neural Networks Extrapolate: From Feedforward to Graph Neural Networkscited by 222
- 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 151
- 2018A micro Lie theory for state estimation in roboticscited by 124
- 2020Flows for simultaneous manifold learning and density estimationcited by 118
- 2020Learning Certified Control using Contraction Metriccited by 49
- 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 45
- 2015Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Designcited by 39
- 2020ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flowscited by 33
- 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
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- 2020Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systemscited by 32
- 2020Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approachcited by 23
- 2021Learning Riemannian Manifolds for Geodesic Motion Skillscited by 23
- 2018Learning Contracting Vector Fields For Stable Imitation Learningcited by 21
- 2021Learning Stable Vector Fields on Lie Groupscited by 12
- 2020Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimizationcited by 11
- 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
- 2019Expected path length on random manifoldscited by 9
- 2021Avoiding Dense and Dynamic Obstacles in Enclosed Spaces: Application to Moving in Crowdscited by 9
- 2022Reaching Through Latent Space: From Joint Statistics to Path Planning in Manipulationcited by 8
- 2018Active Learning based on Data Uncertainty and Model Sensitivitycited by 7
- 2024JacNet: Learning Functions with Structured Jacobianscited by 7
- 2022Reactive Motion Generation on Learned Riemannian Manifoldscited by 6
- 2021Learning Contraction Policies from Offline Datacited by 3
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